Standard Atmosphere final
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School
Georgia Institute Of Technology *
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Course
1601
Subject
Aerospace Engineering
Date
Apr 3, 2024
Type
Pages
9
Uploaded by GeneralBoarMaster702 on coursehero.com
1 AE 1601 –
Standard Atmosphere Activity Turn in on Canvas (Individual) Background Information Andrea Romero AE 1601 The purpose of this exercise is to gain an understanding of planetary atmospheres by comparing the atmospheres of Venus and Mars to the Earth standard atmosphere. Atmosphere profiles for Venus and Mars will be constructed based upon published data obtained by space flight entry probe observations. There are several handy equations and constants used in this exercise. They are listed below. a.
Relation between geometric altitude (
h
G
), geopotential altitude (
h
), and planet radius (
r
P
) 𝑟
𝑃
ℎ
= ℎ
𝐺
𝑟
𝑃
+ ℎ
𝐺
b.
Hydrostatic Equation for Isothermal Layer 𝑝
2 = 𝑝
1
𝑒
−
[
𝑔
0
/(
𝑅𝑇)](ℎ
2
−ℎ
1
) c.
Hydrostatic Equation for Gradient Layer 𝑇
2
−𝑔
0
/(
𝑎𝑅
) 𝑝
2 = 𝑝
1 (
𝑇
)
Note: a is the temperature lapse rate with altitude. d.
Equation of State (Ideal Gas Law) 𝑝
= 𝜌𝑅𝑇
e.
Specific Gas Constants (R): Earth = 287 J/(kg K), Mars = 188.92 J/(kg K), Venus = 188.92 J/(kg K) f.
Planet Radii: Earth = 6,378.14 km, Mars = 3,397.2 km, Venus = 6,051.8 km g.
Gravitational Acceleration at Planet Surface: Earth = 9.8 m/s
2
, Mars = 3.8 m/s
2
, Venus = 8.9 m/s
2
0.
Look up and include the GT honor code statement! 1.
Using the online Georgia Tech Library website (library.gatech.edu), access the “Full
Text Online”
of the following journal article: Seiff, A., “Atmospheres
of Earth, Mars, and Venus, as Defined by Entry Probe Experiments,”
J
Type equation here.
urnal of Spacecraft and Rockets, Vol. 28, No. 3, May-June 1991, pp. 265-275.
𝑝
= 𝑝
(
𝑇
) What is the Digital Object Identifier (doi) number for this article? It is DOI number 10.2514/3.26240 2.
The standard atmosphere for the Earth is modeled as a series of gradient and isothermal regions, as shown in the figure from Anderson’s book (Introduction to Flight). Note that this figure uses
geopotential altitude. Calculate the pressure in the standard atmosphere at 10,000 feet geopotential altitude. You will have to look up the values of the necessary constants in the English unit system. Show your work, and state which hydrostatic equations you use (isothermal/gradient). Watch your units! Intial info used: 10000 ft g=32.2 ft/s^2 R = 1717 ft lb/ (slug*degR) 𝑇
1
=518.7 degR p
1
=2.1162 lb/ft^2 Calculated Slope =a = ∆𝑇
/
∆
h = (390.5 degR-518.7 degR)/(36000 ft-0 ft)=-0.00356 degR/ft Gradient Temperature T(h)=
𝑇
1
+ a(
ℎ
2
−
ℎ
1
)
, then T(10000)=483.1 degR Gradient Pressure 𝑇
2
1
1
−𝑔
𝑇
/(
𝛼∗𝑅
)
P=(2.1162 lb/ft^2*(483.1 degR)/(518.7 degR))^-((32.2 ft/s^2)/(
-0.00356 degR/ft*
(1717 ft lb/ (slug*degR)))
3.
The figure below shows the measured temperature profiles for the Mars atmosphere recorded by the Viking landers. A linear fit (shown in red) has been made to the Viking Lander 1 data, with a single gradient layer from 0 to 40 km, and a single isothermal layer from 40 to 80 km. Note that the altitudes (z) are geometric altitudes. Fill in the missing values from the table. NOTE: You may use Excel for these calculations, but you need to state which equations and which inputs you used to calculate each column. You will need to copy your results onto this worksheet, but please turn in your Excel sheet with your submission
h
G (ft) h (ft) T (R) p (lb/ft^2) (slugs/ft
3
) 0 0 230 7.57E+02 1.7E-05 65616.8 65232.76161 -208.9506324 2.316373405 6.00E-06 131233.6 129706.3848 -824.651752 0.223693921 7.33E-07 196850.4 193434.0446 -1433.229175 0.016536681 5.42E-08 262467.2 256428.6126 -2034.805822 0.001259666 4.13E-09
𝑝
= 𝑝
(
𝑇
) Imperial MARS SI Mars Standard Atmosphere Table: h
G (km) h (km) T (K) p (N/m
2
) (kg/m
3
) 0 0 230 7.50E+02 1.73E-02 20 19.882945 189.76589 110.908369 3.09E-03 40 39.534505 150 10.7105045 3.78E-04 60 58.958695 150 0.79177924 2.79E-05 80 78.159439 150 0.06031303 2.13E-06 er gas constant J/kg K 188.92 formulas used h=rp/(rp+hg)hg density=p/(RT) from 0 -20 m T=T1+a(h-h1) 𝑇
2
1
1
−𝑔
𝑇
/(
𝛼∗𝑅
)
From 20m+ T is a constant and P=p1+e^((g/RT)(h/h1)
data radius ® units km val planet 3397.2 mars for h I used a formula to get t I first need alpha alpha k/km -2.023549 neg means its getting cold
gravity m/s^2 3.8
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